1. Field of the Invention
This invention relates generally to optical systems and, more particularly, to optical systems designed to behave as low pass filters with an adjustable optical cutoff frequency, including the “end-to-end” design of such systems.
2. Description of the Related Art
Electro-optic imaging systems typically include an optical subsystem (e.g., a lens assembly), an electronic detector subsystem (e.g., CCD detector array) and a digital image processing subsystem (e.g., typically implemented in dedicated chips or software). In most electro-optical imaging systems, the spatial sampling rate of the photodetector is well below the diffraction limit of the optical subsystem. In current technology, the smallest pixel dimensions (i.e., pixel-to-pixel pitch) are typically on the order of 3 to 4 microns. The corresponding Nyquist rate associated with such pixel dimensions are between 125 and 166 line pairs per millimeter (lp/mm). It is not uncommon to have optical subsystems with an F# as low as 3 or 4. Given that the diffraction limit is given by 1/(λ F#), diffraction limited optical subsystems can pass image content with spatial frequencies as high as 500 lp/mm in the visible spectrum.
FIG. 1 shows an example of a modulation transfer function (MTF) 110 for an F/4.5 diffraction-limited optical subsystem, the MTF 120 for a 100 percent fill factor 15 micron pitch pixel, and the cumulative MTF 130 for the optical subsystem and detector together. For convenience, the MTF for the optical subsystem will be referred to as the optical MTF 110, the MTF for the detector subsystem as the detector MTF 120, and the combined MTF as the imaging MTF 130. The imaging MTF is the product of the optical MTF and the detector MTF. Also shown is the Nyquist rate for the detector subsystem which is 33 lp/mm in this example. The Nyquist sample rate will also be referred to as the detector sampling frequency. The box 140 indicates the MTF region up to the Nyquist rate. There is a significant fraction of the imaging MTF 130 that lies outside the sampling band 140 (i.e., at frequencies higher than the sampling frequency). Consequently, this electro-optical imaging system has the potential to pass image content with spatial frequencies above the Nyquist rate.
In theory, the image content at higher frequencies could be captured by reducing the pitch of the detector array, thus increasing the detector sampling frequency. However, the ability to shrink pixel dimensions is limited. As pixel dimensions shrink, the dynamic range and signal to noise ratio (SNR) of pixels degrade.
Returning to FIG. 1, when spatial frequency information above the Nyquist rate is sampled, the final image may contain aliasing artifacts such as moiré patterns. The effect of aliasing is even more pronounced in color systems using a single photodetector. In such cases, the color filter pattern reduces the Nyquist rate by a factor of two further exacerbating the problem of aliasing. Researchers have developed a variety of techniques to eliminate aliasing artifacts. To some degree or another, these approaches typically involve some form of discrete component that acts as an optical low pass filter, thus effectively destroying the information content above the Nyquist rate. For instance, Kodak sells an optically transparent plate that is placed directly in front of the detector. The plate has randomly placed particles which introduce random phase errors. This effectively blurs the optical image, thus reducing the content at frequencies above the Nyquist rate and reducing the effects of aliasing.
In another approach, a birefringent plate is used as a discrete low pass filter. The image content is replicated in a color-dependent fashion using the spatial shifting property of the birefringent plate. The birefringent plate replicates the point spread function of the optical subsystem but shifted with respect to the original point spread function. The cumulative point spread function created by the original and its shifted versions can span one or two pixel widths. This replication effectively blurs the optical image to reduce frequency information above the Nyquist rate. However, such optical low pass filters often are wavelength dependent.
In yet another approach, CDM Optics of Boulder, Colo. developed a specially designed component: a phase plate that is placed at the aperture of the optical subsystem in order to encode the incoming wavefront in a particular way. Digital image processing is used later to reverse the encoding introduced by the phase plate and retrieve certain image content. However, the CDM approach appears to work for only certain types of artifacts and it can produce overly smooth images.
One drawback of these approaches is that an additional component is added to the optical subsystem, thus increasing the complexity and cost. Another drawback is that these components typically are designed for a specific situation. If the optical subsystem is itself adjustable for use over a range of situations (different F#'s, focal lengths, etc.), or can be used with a variety of different detector subsystems and/or digital image processing subsystems, a single one of these components may not be flexible enough to accommodate the various situations and adjustable versions of these components may not be available.
Thus, there is a need for approaches that can reduce aliasing effects, but in a manner that overcomes some or all of the above drawbacks.